A220469 Fibonacci 14-step numbers, a(n) = a(n-1) + a(n-2) + ... + a(n-14).

1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16383, 32765, 65528, 131052, 262096, 524176, 1048320, 2096576, 4193024, 8385792, 16771072, 33541120, 67080192, 134156288, 268304384, 536592385, 1073152005, 2146238482, 4292345912, 8584429728

Offset

1,3

Comments

Also called tetradecanacci numbers. In previous similar sequences, a(1),...,a(n-1) have been set equal to zero and a(n)=1. For example, A168084 (Fibonacci 13-step numbers) has 12 0's as the first 12 terms and a(13)=1.

Links

Table of n, a(n) for n=1..35.

M. Janjic, On Linear Recurrence Equations Arising from Compositions of Positive Integers, J. Int. Seq. 18 (2015) # 15.4.7

Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4

Index entries for linear recurrences with constant coefficients, signature (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1).

Mathematica

FibonacciSequence[n_, kMax_] := Module[{a, s}, a = Join[{1}, Table[0, {n - 1}]]; lst = {}; Table[s = Plus @@ a; a = RotateLeft[a]; a[[n]] = s, {k, 1, kMax}]]; FibonacciSequence[14, 50] (* T. D. Noe, Feb 20 2013 *)
Drop[LinearRecurrence[PadRight[{}, 14, 1], Join[PadRight[{}, 13, 0], {1}], 50], 13] (* Harvey P. Dale, Feb 25 2013 *)
LinearRecurrence[{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096}, 35] (* Ray Chandler, Aug 03 2015 *)

Crossrefs

Cf. A000045 (Fibonacci), A000073 (tribonacci), A000078 (tetranacci), A001591 (pentanacci).

Sequence in context: A216095 A190126 A219676 * A370254 A328679 A220051

Adjacent sequences: A220466 A220467 A220468 * A220470 A220471 A220472

Keyword

nonn

Author

Ruskin Harding, Feb 20 2013

Status

approved